# Rate-Optimal Noise Annealing in Semi-Dual Neural Optimal Transport: Tangential Identifiability, Off-Manifold Ambiguity, and Guaranteed Recovery

arXiv: https://arxiv.org/abs/2602.04110 · HTML: https://mlsanity.com/paper/2602.04110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Statistical optimal transport](https://mlsanity.com/paper/2407.18163/) (2024)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space](https://mlsanity.com/paper/1910.05954/) (2019)
- [Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport](https://mlsanity.com/paper/2402.05443/) (2024)
- [Intrinsic Dimension Estimation Using Wasserstein Distances](https://mlsanity.com/paper/2106.04018/) (2021)
- [An Optimal Transport Perspective on Unpaired Image Super-Resolution](https://mlsanity.com/paper/2202.01116/) (2022)
- [Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan](https://mlsanity.com/paper/2502.04583/) (2025)

## Built on by (most cited first, 1 of 1)

- [Neural Optimal Transport in Hilbert Spaces: Characterizing Spurious Solutions and Gaussian Smoothing](https://mlsanity.com/paper/2602.14086/) (2026)

## Abstract (arXiv)

Semi-dual neural optimal transport learns a transport map via a max-min objective, yet training can converge to incorrect or degenerate maps. We fully characterize these spurious solutions in the common regime where data concentrate on low-dimensional manifold: the objective is underconstrained off the data manifold, while the on-manifold transport signal remains identifiable. Following Choi, Choi, and Kwon (2025), we study additive-noise smoothing as a remedy and prove new map recovery guarantees as the noise vanishes. Our main practical contribution is a computable terminal noise level varepsilonstat(N) that attains the optimal statistical rate, with scaling governed by the intrinsic dimension m of the data. The formula arises from a theoretical unified analysis of (i) quantitative stability of optimal plans, (ii) smoothing-induced bias, and (iii) finite-sample error, yielding rates that depend on m rather than the ambient dimension. Finally, we show that the reduced semi-dual objective becomes increasingly ill-conditioned as varepsilon downarrow 0. This provides a principled stopping rule: annealing below varepsilonstat(N) can textitworsen optimization conditioning without improving statistical accuracy.